Far be it for me to advise on hotel choices (different people have different tastes) but Conrad is a long way from anywhere, which is awkward given the time it takes to get anywhere through Istanbul traffic. Moreover, the word "Conrad" is Turkish taxi-driver dialect for "please take me by the scenic route and invent surcharges".

I think you can get better value staying in one of the old, small hotels in Sultanahmet where all the sights are walkable and you have plenty of choice for eating and drinking in nearby cafes. My personal fave is Naz Wooden House. But YMMV.